log^3(3x+8)=log^3(x^2+x)

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Solution for log^3(3x+8)=log^3(x^2+x) equation: 


Simplifying
log3(3x + 8) = log3(x2 + x)

Reorder the terms:
g3lo(8 + 3x) = log3(x2 + x)
(8 * g3lo + 3x * g3lo) = log3(x2 + x)
(8g3lo + 3g3lox) = log3(x2 + x)

Reorder the terms:
8g3lo + 3g3lox = g3lo(x + x2)
8g3lo + 3g3lox = (x * g3lo + x2 * g3lo)
8g3lo + 3g3lox = (g3lox + g3lox2)

Solving
8g3lo + 3g3lox = g3lox + g3lox2

Solving for variable 'g'.

Move all terms containing g to the left, all other terms to the right.

Add '-1g3lox' to each side of the equation.
8g3lo + 3g3lox + -1g3lox = g3lox + -1g3lox + g3lox2

Combine like terms: 3g3lox + -1g3lox = 2g3lox
8g3lo + 2g3lox = g3lox + -1g3lox + g3lox2

Combine like terms: g3lox + -1g3lox = 0
8g3lo + 2g3lox = 0 + g3lox2
8g3lo + 2g3lox = g3lox2

Add '-1g3lox2' to each side of the equation.
8g3lo + 2g3lox + -1g3lox2 = g3lox2 + -1g3lox2

Combine like terms: g3lox2 + -1g3lox2 = 0
8g3lo + 2g3lox + -1g3lox2 = 0

Factor out the Greatest Common Factor (GCF), 'g3lo'.
g3lo(8 + 2x + -1x2) = 0

Factor a trinomial.
g3lo((4 + -1x)(2 + x)) = 0


Subproblem 1
Set the factor 'g3lo' equal to zero and attempt to solve:

Simplifying
g3lo = 0

Solving
g3lo = 0

Move all terms containing g to the left, all other terms to the right.

Simplifying
g3lo = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

Move all terms containing g to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Add 'x' to each side of the equation.
-1x + x = -4 + x

Combine like terms: -1x + x = 0
0 = -4 + x

Simplifying
0 = -4 + x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

Move all terms containing g to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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